Soon after the discovery of pulsars, it was realised that the
observed sample is heavily biased towards the brighter objects
that are the easiest to detect. What we observe therefore most
likely represents only the tip of the iceberg of a much larger
underlying population [88]. The extent to which the sample is incomplete is well
demonstrated by the projection of pulsars onto the Galactic plane
and their cumulative number distribution as a function of
distance shown in Fig.
12
. Although the clustering of sources around the Sun seen in the
left panel of Fig.
12
would be consistent with Ptolemy's geocentric picture of the
heavens, it is clearly at variance with what we now know about
the Galaxy, where the massive stars show a radial distribution
about the Galactic center.

Figure 12:Left: The sample of radio pulsars from the Princeton
catalog [196] projected onto the Galactic plane. The Galactic center is at
(0,0) and the Sun is at (-8.5,0). Right: Cumulative number of
observed pulsars (solid line) as a function of projected
distance,
d. The dashed line shows the expected distribution for a model
population (see text).

The extent to which the pulsar sample is incomplete is shown
in the right panel of Fig.
12
where the cumulative number of pulsars is plotted as a function
of the projected distance from the Sun. The observed distribution
is compared to the expected distribution for a simple model
population in which there are errors in the distance scale, but
no selection effects. We see that the observed sample becomes
strongly deficient in terms of the number of sources for
distances beyond a few kpc. We now discuss the main selection
effects that hamper the detection of pulsars in some detail.